Acyclic 5-Choosability of Planar Graphs Without Adjacent Short Cycles

被引：12
|
作者：
Borodin, O. V. [1 ,2 ]
Ivanova, A. O. [3 ]
机构：
[1] Russian Acad Sci, Inst Math, Siberian Branch, Novosibirsk 630090, Russia
[2] Novosibirsk State Univ, Novosibirsk 630090, Russia
[3] Yakutsk State Univ, Inst Math, Yakutsk 677891, Russia
来源：
JOURNAL OF GRAPH THEORY | 2011年 / 68卷 / 02期
基金：
俄罗斯基础研究基金会;
关键词：
planar graph; acyclic coloring; acyclic choosability; COLORINGS; 4-CYCLES; GIRTH;
D O I：
10.1002/jgt.20549
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The conjecture on acyclic 5-choosability of planar graphs [Borodin et al., 2002] as yet has been verified only for several restricted classes of graphs. None of these classes allows 4-cycles. We prove that a planar graph is acyclically 5-choosable if it does not contain an i-cycle adjacent to a j-cycle where 3 <= j <= 5 if i = 3 and 4 <= j <= 6 if i = 4. This result absorbs most of the previous work in this direction. (C) 2010 Wiley Periodicals, Inc. J Graph Theory 68: 169-176, 2011
引用
收藏
页码：169 / 176
页数：8
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